First, double check that you entered your API key correctly. After signing in to Revue, you can see your API key at the bottom of the integrations page.

If the integration still doesn't work, your Revue account might need to be reviewed first. You can trigger the review process by importing a list of subscribers. Go to the subscribers page, click "Add subscribers", then click "Import from file." If you don't have a file to upload, you can enter one of your own email addresses.

Important: while your account is being reviewed, you may be unable to send issues. So you may want to wait until right after you send out one of your regular issues before you import subscribers.

(Although Revue's API documentation doesn't talk about this, this is what they said in an email:)

It appears your account has yet to be verified. Account verification is now required to add an API to your account. You can upload a subscriber list via the Revue Import system. Once approved, you'll receive API access.